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The generator is defined correctly, but you're not using it in the right way.
Expression count() creates a new instance of the generator; so the first time you call next() it will give zero.
Instead, you should create it once, and then call next() several times on the resulting object, e.g.:
sage: mycount = count()
sage: [mycount.next() for i in range(18)]
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]
sage: mycount = count()
sage: [next(mycount) for i in range(18)]
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]
sage: next(mycount)
18
sage: next(mycount)
19
